A potential-based particle method for failure modeling in solids

Continuum mechanics is typically based on the fundamental notion of a mesoscopic volume element, whose physical characteristics can be considered as averaged properties over discrete particles, obeying deterministic relationships. Recent works on granular-like materials have found that a continuum description may not be appropriate for these cases, since inhomogeneities at the particle level, such as force chains and microscopic breaking, can occur. The above discussed aspects point out the particle nature of materials and suggest to use a different approach, namely a discrete one, to describe their mechanical behaviour; moreover such a new approach can be suitably used for both continuum-like or granular-like materials by properly setting the nature of the reciprocal forces exerted between particles. Such an approach is usually identified also as the discrete-element method (DEM). By properly modelling the material as an assemble of small discrete elements, the mechanical behaviour and the failure evolution of the material under mechanical actions can be properly described. In the present paper, a computational discrete element method for continuum or particle-like materials, based on the concept of potential-based force interaction law for the quantification of the mutual forces exchanged by small portions of the material interacting each other, is developed. After illustrating the basic concepts related to the discrete nature of materials and their mechanical modelling, a simple particle based approach is presented by adopting a Lennard-Jones like potential function to quantify the particles interaction. Finally, an example related to the failure of a brittle solid is analysed in order to underline the capability of the proposed approach.